Snow falls on tourists stopping in front of the White House in Washington, last week.

Pablo Martinez Monsivais/AP

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Should the Obama administration allow Donald Trump to pay for the resumption of White House tours? That’s an issue today because the popular walk-throughs have been canceled due to the "sequester," and the mogul/TV star has indeed offered to keep the doors open at the nation’s executive mansion.

The Secret Service ordered the suspension of the tours to save on agent overtime, according to White House officials. It’s true that the money at issue isn’t that much in the context of the federal budget or a billionaire’s balance sheet: only about $72,000 a week, at most.

This has led to lots of Republicans charging that the White House is playing a variation of the old Washington Monument game by denying school kids their preplanned White House visits. Previously an administration, facing budget cuts, announces with great fanfare that the Washington Monument will be closed until further notice. The White House can’t do that this time because the monument is already shut because of earthquake damage. So they’ve moved on to another popular D.C. symbol, the White House, for the same political effect, in the GOP view.

Rep. Louie Gohmert (R) of Texasoffered an amendment on the floor the other day to ban President Obama’s golf games in the name of restarting the tours. Rush Limbaugh complained that the White House closed the tours, then spent lots of Secret Service money for a caravan that drove the president half a mile to an outreach dinner with GOP lawmakers.

“They wanted people sad and let down, and they wanted people blaming the Republicans for it. And it’s backfiring, not working,” Mr. Limbaugh said on his show.

The “we’ll pay for it” meme started late last week. First Fox host Eric Bolling said he’d pay for a week of tours. Then fellow talking head Sean Hannity said he’d do the same. Newt Gingrich on Twitter suggested Trump could keep the doors open for school kids indefinitely.

Some news reports suggested over the weekend that Trump had agreed – if nemesis Bill Maher chipped in, too. But during Monday’s Fox appearance, Trump said he’d heard about Newt’s suggestion only when the Friends asked him.

The sequester, Mr. Earnest pointed out, mandates across-the-board cuts that administrators have little flexibility in carrying out. With a political jab, he noted that many of the people calling for private tour funding also called the overall imposition of the sequester cuts a victory for Republicans.

Others note it’s possible that the offer to pay for the tours could backfire.

For one thing, if tours, why not education funds for poor kids? Lots of things are being cut, fairly or not. Democrats might start asking if the GOP’s offers reflect a socioeconomic bias.

And even if (though?) the White House has been overly dramatic about the impact of the sequester, real hardship will eventually occur at federal installations across the country. In the National Journal, national correspondent Jill Lawrence notes that local media across the country are beginning to report on the effects of the cuts on local airports, food banks, parks, and schools.

While the administration has been maladroit, “the barely suppressed GOP glee at the White House fumbles, and the cavalier acceptance of the sequester by some Republicans, is also bound to backfire,” Ms. Lawrence writes.